# Photonic Crystal Simulation

Photonic crystals are periodic structures that are designed to affect the motion of photons in a similar way that periodicity of a semiconductor crystal affects the motion of electrons. The non-existence of propagating EM modes inside the structures at certain frequencies introduces unique optical phenomena such as low-loss-waveguides, omni-directional mirrors and others. The part of the spectrum for which wave propagation is not possible is called the optical band-gap. The underlying physical phenomenon is based on diffraction. Therefore, the lattice constant of the photonic crystal structure has to be in the same length-scale as half the wavelength of the electromagnetic wave. Figure 1 shows a one dimensional periodic structure which is investigated by using the transient solver of CST MICROWAVE STUDIO® (CST MWS).

Figure 1: 1 dimensional periodic structure

The rods are made from GaAS with refractive index of 3.4 and with an edge length of about 180 nm. The lattice spacing between the rods is 760 nm. As a first step, the transmission of a plane wave through this crystal is simulated.

Figure 2: single column of the array

By using appropriate boundary and symmetry conditions it is sufficient to calculate a single column of this array as shown in Figure 2. In this case, the structure is driven by a waveguide port. Due to the magnetic and electric symmetry planes, the excitation mode is a normally incident plane wave.

Figure 3: Transmisson vs. wavelength

Figure 3 shows the transmission through the structure. Between 1400 and 2200 nm the transmission is zero. In this bandgap region no wave propagation in possible.

Figure 4: Wave Propagation at frequencies below the band gap

Figures 4-6 shows the propagation of a plane wave at normal incident for at different frequencies.

Figure 5: Wave propagation at frequencies in the band gap

Figure 6: Wave Propagation at frequencies above the band gap

The information obtained about the photonic band gap can be used to design optical devices. Figure 7 shows the periodic PBG structure as described above. A line defect is introduced and the structure is excited with a electromagnetic wave at band gap frequencies. The wave can only propagate inside the line defect.

Figure 7: Photonic Crystal with line defect

Finally, Figure 8 shows the wave propagation inside the Photonic crystal with a bent defect. Again, the structure is driven with a time harmonic signal. The signal frequency is inside band gap of the crystal. Consequently, the wave propagates inside bend defect.

Figure 8: Photonic crystal with a bend defect

This article demonstrates the possibilities to model photonic crystals with CST MWS by using the transient solver. The general characterization would also be possible with the Frequency Domain and Eigenmode Solver of CST MWS by applying periodic boundary conditions.

CST Article "Photonic Crystal Simulation"

last modified 15. Jan 2007 5:42

printed 24. Apr 2014 8:41, Article ID 296

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